Informatics and Applications
2019, Volume 13, Issue 4, pp 4853
THE MEAN SQUARE RISK OF NONLINEAR REGULARIZATION IN THE PROBLEM OF INVERSION OF LINEAR HOMOGENEOUS OPERATORS WITH A RANDOM SAMPLE SIZE
Abstract
The problems of constructing estimates from observations, which represent a linear transformation of the initial data, arise in many application areas, such as computed tomography, optics, plasma physics, and gas dynamics. In the presence of noise in the observations, as a rule, it is necessary to apply regularization methods. Recently, the methods of threshold processing of wavelet expansion coefficients have become popular. This is explained by the fact that such methods are simple, computationally efficient, and have the ability to adapt to functions which have different degrees of regularity at different areas. The analysis of errors of these methods is an important practical task, since it allows assessing the quality of both the methods themselves and the equipment used. When using threshold processing methods, it is usually assumed that the number of expansion coefficients is fixed and the noise distribution is Gaussian. This model is well studied in literature and optimal threshold values are calculated for different classes of signal functions. However, in some situations, the sample size is not known in advance and has to be modeled by a random variable. In this paper, the author considers a model with a random number of observations containing Gaussian noise and estimates the order of the meansquare risk with an increasing sample size.
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[+] About this article
Title
THE MEAN SQUARE RISK OF NONLINEAR REGULARIZATION IN THE PROBLEM OF INVERSION OF LINEAR HOMOGENEOUS OPERATORS WITH A RANDOM SAMPLE SIZE
Journal
Informatics and Applications
2019, Volume 13, Issue 4, pp 4853
Cover Date
20191230
DOI
10.14357/19922264190408
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; threshold processing; linear homogeneous operator; random sample size; mean square risk
Authors
O. V. Shestakov ,
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 152 Leninskiye Gory, Moscow 119991, GSP1, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
